How much wiring did you eliminate to go drag racing?
With a car that old, I would suspect the turn signal switch needs attention, but then again, if it doesn't connect to anything, even a NOS one isn't going to work.
The 4 way and the turn signals are separate circuits, you need to test each one independently of each other. The only things they share is the turn signal switch (each has its own part in the turn signal switch) and the wiring to the bulbs and the bright filament on the bulbs
It could be as easy as a fuse, or flasher unit. I'd start with those, and make sure the simple stuff is good.